This invention relates to the display of the response characteristics of an array of seismic sources, and more particularly to an improved display of the response characteristics as a function of the azimuth and depth relative to the array.
In seismic exploration, an array of seismic sources is moved along a line of exploration on the earth's surface. The reflections and/or refractions of seismic energy from the sources are recorded as seismograms. Complex source and receiver arrays have been successfully used to suppress noise and emphasize reflections or refractions from particular areas of interest. Seismic energy from an array of sources adds cumulatively, or the energy is cancelled, at particular points relative to the array. By appropriate selection of the number of sources in the array, the spacing of the sources, and the timing of firing, improved seismograms can be obtained. Particularly in marine seismic exploration, the presence of a homogeneous near surface water layer, combined with potential scatterers, such as channels, faults, salt domes, drilling rigs, and so on, on or near the water bottom, favors the use of an array having a relatively unattenuated propagation of energy which is off the line of exploration.
In an attempt to use the best possible array of sources in gathering seismograms, a great deal of study has been directed to the response characteristics of seismic arrays. See "Toward an Understanding and Suppression of Coherent Noise in Marine Seismic Data," by K. Larner, R. Chambers, M. Yung, W. Lynn, and W. Wai, Paper presented at the 51th Annual International SEG Meeting, Nov. 9-11, 1981, Los Angeles; and "Electroacoustic Characteristics of Marine Seismic Streamers, by J. W. Bedenbender, R. C. Johnston, and E. B. Neitzel, GEOPHYSICS, Vol. 35, p. 1054-1072, 1970.
The response characteristics of an array of sources can be physically measured, or they can be determined from the characteristics of the array itself. Physical measurement of the response characteristics requires taking the array to very deep water where there will be no obscuring reflections and measuring the amplitude of the seismic energy at various locations differing in azimuth and dip. Because this is a laborious procedure, the response characteristics of an array are more often determined from the physical parameters of the array itself. The response of an acoustic array is related to its parameters, and to the azimuth .phi. and to the dip .theta. by the following: ##EQU1## where: Aj=strength of jth point source element
(xj, yj)=location of jth point source element PA0 N=number of point source elements in the areal array PA0 f=frequency of consideration PA0 v=near surface Seismic Velocity
In order to provide a display of the response characteristics of an array of sources, the prior art usually finds the Fourier transform of the amplitude response in one or two dimensions. The amplitude response may be displayed in the wave number domain, k.sub.x vs.k.sub.y, with contours of amplitude, sometimes expressed in decibels. Alternatively, the displays are made in direction for one frequency so that traditional one dimensional plots can be made.
The first mentioned display contains all of the required information, but it is in a form which cannot be immediately used. The second mentioned method requires the production of many plots and these are difficult to evaluate quickly.
It is an object of the present invention to provide a display of the amplitude characteristics of an array of seismic sources in a form which can be readily interpreted.
It is a further object of the present invention to provide a display of the response characteristics of an array of seismic sources in a form which can be quickly used by a geophysicist to select the proper source array for exploration of a given area of interest.